Reading between the lines: some simple maths in the time of COVID-19

By Sara Loo

You don’t need me to tell you that things are not as they used to be. Unless you have recently emerged from a 3-month long hike, you should be well aware of the current global atmosphere. Working from home, social distancing, lockdown. Words that have entered our everyday vernacular. There is a never-ending stream of news and updated case numbers, late night press conferences and a continually changing list of do’s and don’ts.

Staying informed is important. But in these anxious times, keeping up to date can be exhausting. I have seen more scientific terms in the news than ever, and have been sent articles from family and friends with words I thought were confined to the depths of my research, never to see the light of day.

To non-mathematicians, there is a long list of scientific and mathematical terms to be understood, and just So. Much. News. COVID-19 has taken over the news cycle. And, with it come phrases like enveloped viruses, antivirals, doubling time, mortality and morbidity, exponential growth.

Though I do not by any means claim to be an expert in viral epidemiology, I currently work in understanding the evolution of infectious diseases and can claim to knowing something or other about mathematics. And there may be no better time than now to spread the good news of mathematics and its usefulness to our everyday lives.

Exponential growth

An exponential graph can be scary to look at. When we’re tracking cases of a disease and seeing it get larger, and then get larger even quicker, it’s easy to see how the changing numbers may fan our fear.

However, it’s important to note that exponential growth has its limits, and can be slowed by employing certain preventative measures, as we’ve seen in countries such as Singapore, Japan and South Korea – countries that seem to have successfully ‘flattened the curve’.

Even in the most dire case, the curve will flatten when everyone has become infected; when there’s no one else left to infect.

As an example of exponential growth slowing down, let’s take for example your productivity during a day of working from home. You might start the day with the goal of writing a scientific manuscript, or a blog piece. It might be slow to get going. Other than the inevitable writer’s block, there’s that second coffee you need to go to the kitchen to make, and a child’s IT issues to fix so they can join their online class.

Once you have that hot cuppa and you’ve told your child to “try turning it off and on again”, you get to sit down and focus. Then, the writing just starts. Words flow quickly.

But then you have lunch, and you accidentally eat too much of last night’s leftover pasta. Your kids get more and more irritable as they get bored of being cooped up in front of their computer screen, starting to throw said leftover pasta at each other. Things get crazy at home.

Your manuscript sits forgotten for a time. Nothing new is written. After returning to your desk, you start typing, but slowly. The excess carbs slow your thinking. The length of your article still grows, but slowly.

Like the speed of your writing in a day of working from home, we want to slow down the spread of infection. We want to impose a post-lunch carbo crash onto the outbreak. We want to reduce new cases quickly.

SIR modelling

You may have seen this simulation of little dots getting infected with COVID-19, and the effects of social distancing on the overall spread of the outbreak (if you haven’t, please do. It’s a great visualisation). This is based on a simple mathematical model commonly used in epidemiology known as an SIR model.

The letters stand for Susceptible, Infectious, and Recovered.  Individuals can be susceptible to a disease, be infected by a disease, or have recovered from that disease.

Mathematical modelling is based around tracking changes to different categories of things (in this case, categories of people and their state based on whether they have a certain disease or not), assuming these changes follow a set of average behaviours. An SIR model follows this basic structure.

Based on what we know about these average behaviours, how will the outbreak progress?

An example SIR model, with mathematical detail for those so inclined

If 1 infected individual, say, hops off a plane into Sydney Airport, will an outbreak in Sydney? If there are 100 people in the arrival hall of the airport at the time they arrive, and we know the disease is transmissible at a certain rate, will there be an outbreak in Sydney?  

Will all the susceptible individuals become infectious, provided they move from susceptible to infectious at a certain rate (β)?


Understanding how quickly the outbreak progresses in infectious disease modelling revolves around a value called R0 (pron. arr-naught). The basic description of R0 is that it is a measure of the average number of new infections every infected individual is likely to cause.

Without going into the mathematical details, this is often dependent on the population size, the rate of transmission (how easy it is to transmit – i.e. can I get it by just touching the same elevator button as someone who is sick, or do they need to sneeze directly into my mouth), and how many other people are around that are likely to get sick too.

Numerically, an R0 greater than 1 indicates that a disease will spread throughout a population. Public health initiatives aim to reduce this value to less than 1, in order to minimise the effect of a disease outbreak and eliminate it from a population.

#stayhome aims to reduce this R0 by effectively removing people from the population. If they’re infected they can’t infect any more people. If they’re susceptible, they can’t get infected and subsequently infect more people.

You may have seen this represented in the form of match sticks, dominoes, or a family-tree-like transmission chain. Whatever the medium you’ve seen the information conveyed, the message is the same. If possible, stay home. It may not be possible for everyone, but for those who can: stay home.

While we are living in uncertain times, and though mathematics has the reputation of being stressful and equally anxiety-inducing, the numbers and predictions you see in the news are based on well-studied models. I, for one, take comfort in that.

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Medicine, microbiomes and mutations – Meet Natalia

Interview by Sara Loo

Understanding cancer has been on the heart of Early Career Champion Natalia Castaño Rodríguez ever since she was a clinician in her home country of Colombia. She moved to Sydney in 2009 to pursue research and has quickly established herself as an emerging player in the field of immunogenetics and gastric cancer. On top of her research, she has proven to be a leader in the School of Biotechnology and Biomolecular Sciences at UNSW and keeps herself busy as Chair of the UNSW Early Career Academic Network. At the beginning of this year, Natalia was awarded two fellowships – a credit to her passion for her work and her driven nature. We asked her a few questions this week to learn more about her journey so far.


You recently finished up as a National Health and Medical Research Council Early Career Fellow and were also just awarded a Cancer Institute NSW Early Career Fellowship and a UNSW Scientia Fellowship. Firstly, congratulations on your success! Can you explain your research to us?

I have been investigating the interplay between host mutations, the immune system and gastrointestinal microbiomes (i.e. the community of microorganisms that inhabit a particular environment) and their effects on gastrointestinal tumours (like gastric and oesophageal cancer) and other chronic inflammatory conditions such as Crohns’ disease and ulcerative colitis.

I have recently received important funding to further my investigations on gastric cancer. We have identified particular mutations in genes involved in the innate immune response that dramatically increase the risk of gastric cancer in three different ethnic groups (East Asians, South Americans and Caucasians). Investigating these mutations will allow us to identify those who are genetically susceptible to developing gastric cancer and, if they are infected with Helicobacter pylori (which is the main risk factor for gastric cancer) selectively treating them for the infection and closely surveying them. This is highly relevant for disadvantaged communities including those living in developing countries and Aboriginal communities in Australia, in whom gastric cancer is highly prevalent.

My work is particularly focussed on autophagy, which is defined as a degradation process in which external material is taken up by and degraded within the cell. Our investigations will hopefully help us identify autophagy-related host factors involved in the regulation of the gastric microbiome. We want to increase our understanding of microbially-disrupted autophagy (via Helicobacter pylori and other bacteria likely to cause cancer) and its contribution to gastric cancer and chemoresistance, which could be translated into potential therapeutic targets.


What are you most excited by in this fast-growing field of cancer genetics and the microbiome?

The combination of host mutations, environmental factors and microorganisms in the gastrointestinal tract contribute to the development of gastrointestinal cancers and other chronic inflammatory conditions. With current technologies, it is now possible to collectively characterise and quantify pools of biological molecules (DNA, RNA, proteins and metabolites) of an organism or many organisms simultaneously. I trust this will help us identify robust biomarkers and therapeutic targets for these diseases in the near future.


What does your average day look like (at work and outside of work)?

I guess the first thing that it would be important to point out is that when you work in research you don’t have a 9-5 job, you are in the lab as long as you need to be, even if that sometimes means late nights and weekends. And even if we are not physically in the lab, we are always connected somehow via email or working on something at home. But this doesn’t mean that we can’t have a balanced life; we can, and we do, and our universities are currently working very hard to teach us how to have fulfilling lives without compromising our research output. Happy researchers are more likely to be successful at publishing and getting funding, which are normally the parameters used to evaluate our performance.

A standard day involves waking up early to exercise and to have enough time to talk to my parents on the phone. They both live in Colombia but as a classic Latin American family, we are extremely close. Then, I get to work at 9-10am to first discuss with my students about the experiments that they will be doing or any other concerns. Then, I usually move to my desk to answer urgent emails, analyse data or continue writing something (e.g. a manuscript, grant application, fellowship application, promotion application, reviewing someone else’s work). It is also normal to have one or two meetings scheduled either with collaborators, committees or my own students. Between 4-7:30 pm, I usually return to my desk to try to continue writing or to focus my attention on lab management tasks (e.g. accounting, orders, safety, etc.). I will then meet my husband, who is also a medical researcher at UNSW, to walk back home while we discuss our days and what’s for dinner.

Outside work, I am passionate about dogs, outdoor activities (particularly speed skating) and dancing. Most importantly, I am very lucky to have a wonderful husband who shares my work and personal interests.

Natalia celebrating her recent achievements with two of her group members, Isidora Simovic (also a Women in Maths and Science Champion) and Apeksha Goswami, and her mentor Prof Hazel Mitchell, first-ever female professor in the School of BABS.

I’m curious about your journey so far. What brought you to UNSW? You transitioned from being a clinical doctor to research – what initiated that change?

My story started in 2009, following the completion of my Doctor of Medicine degree in Colombia.  I decided to leave my home country to come to Australia and pursue my dream of becoming a clinician researcher by undertaking a Masters degree, which was followed by a PhD. As an international student, I was fortunate enough to receive a number of scholarships from Colombia and Australia to be able to fund these studies. At the time, I was also very lucky to have an excellent supervisor and mentor, Prof Hazel Mitchell. She was extremely supportive and quickly became a role model, as the first female professor in the School of BABS.

I was then awarded an Early Career Fellowship by the National Health and Medical Research Council to expand my work on the role of the immune system and genetic factors, particularly related to pattern recognition receptors (host sensors that detect pathogens) and autophagy, in gastric cancer (2016- 2020). I was further awarded a Cancer Australia Priority-driven Collaborative Cancer Research Scheme Young Investigator Grant (2017) as well as a Gastroenterology Society of Australia Project Grant (2019) to investigate the contribution of dysregulated autophagy to the development of gastric cancer. More recently, I was awarded a Cancer Institute NSW Early Career Fellowship and a UNSW Scientia Fellowship to continue my investigations and cement myself as an emerging leader in the field.


You’ve clearly established yourself as a serious and successful scientist! Have you always been interested in science? Are there any memories that inspired you to be a doctor and/or get a PhD?

I have always been interested in immunogenetics of cancer, even as a young medical student who lived in Colombia, a developing country with limited research potential. My first research project while I was a medical student was on immunotherapy for melanoma. However, it was probably the death of a young patient presenting with pancreatic cancer who was assigned to me during a rotation in internal medicine, that made me realize that I wanted to dedicate my life to cancer research to find ways to prevent the disease and improve the quality of life and survival rates of patients. More recently, I was personally affected by the death of a close friend who was only 33 when she lost her battle against lung cancer. Her bravery was an example to me and made me feel more committed than ever to cancer research.


What inspired you to be a UNSW Maths and Science Champion?

I believe that the UNSW Women in Maths and Science Champions Program is a unique opportunity to consolidate essential skills for good and effective leadership, and improved communications skills to share your research with the wider community and the next generation of female researchers. I also believe this program is important to network with other vibrant female researchers and foster collaborations to promote, enhance and complement areas of research led by women at UNSW.


What should we be doing more of in society to promote women in STEM? 

To showcase successful young females involved in STEM is a powerful tool to bring down stereotypes and show our girls that they can also be researchers, mathematicians, doctors, etc. However, I cannot stop myself from thinking that we need to do more. As long as our governments don’t invest more in female education, our impact will always be limited. This is particularly important in developing countries, where access to higher education is difficult and extremely expensive.


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